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Title: A modal approach for the gyroscopic quadratic eigenvalue problem
Language: English
Authors: Voß, Heinrich 
Elssel, Kolja 
Keywords: Quadratic eigenvalue problem;gyroscopic eigenproblem;automated multilevel
Issue Date: Mar-2004
Source: Proc. of ECCOMAS 2004, Jyväskylä, Finland 2004. ISBN 951-39-1869-6
Abstract (english): 
The Automated Multi-Level Substructuring (AMLS) has been developed to reduce the computational demands of frequency response analysis. AMLS automatically divides a large finite element model into many substructures on a number of levels based on the sparsity structure of the system matrices. Assuming that the interior degrees of freedom depend quasistatically on the interface degrees of freedom, and modeling the deviation from quasistatic dependence in terms of a small number of selected substructure eigenmodes the size of the finite element model is reduced substantially. In this paper we consider conservative gyroscopic eigenvalue problems. The original AMLS method neglects the gyroscopic effects. We generalize the AMLS approach taking advantage of the fact that for gyroscopic problems there exists a basis of eigenvectors which can be used when modeling the deviation from quasistatic behaviour. In both cases the resulting quadratic eigenproblem is still very large. We suggest to solve it by the nonlinear Arnoldi method taking advantage of the minmax characterization of its eigenvalues.
DOI: 10.15480/882.65
Institute: Mathematik E-10 
Document Type: Chapter/Article (Proceedings)
License: In Copyright In Copyright
Part of Series: Preprints des Institutes für Mathematik 
Volume number: 73
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